Numerical simulation of elliptical particles sedimentation in power-law fluid using the improved smoothed profile-lattice Boltzmann method

References

• Aghakhani, S., A. Hajatzadeh Pordanjani, A. Karimipour, A. Abdollahi, and M. Afrand. 2018. Numerical investigation of heat transfer in a power-law non-Newtonian fluid in a C-shaped cavity with magnetic field effect using finite difference lattice Boltzmann method. Computers & Fluids 176:51–67. doi: 10.1016/j.compfluid.2018.09.012.
   Web of Science ®Google Scholar
• Aidun, C. K., and J. R. Clausen. 2010. Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics 42 (1):439–72. doi: 10.1146/annurev-fluid-121108-145519.
   Web of Science ®Google Scholar
• Aidun, C. K., Y. Lu, and E. J. Ding. 1998. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. Journal of Fluid Mechanics 373:287–311. doi: 10.1017/S0022112098002493.
   Web of Science ®Google Scholar
• Amiri-Delouei, A., M. Nazari, M. Kayhani, and G. Ahmadi. 2016. A non-Newtonian direct numerical study for stationary and moving objects with various shapes: An immersed boundary-lattice Boltzmann approach. Journal of Aerosol Science 93:45–62. doi: 10.1016/j.jaerosci.2015.11.006.
   Web of Science ®Google Scholar
• Amiri-Delouei, A., M. Nazari, M. H. Kayhani, S. K. Kang, and S. Succi. 2016. Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach. Physica A: Statistical Mechanics and Its Applications 447:1–20. doi: 10.1016/j.physa.2015.11.032.
   Web of Science ®Google Scholar
• Bisht, M., and D. V. Patil. 2017. Power-law fluid flow in driven enclosures with undulation using MRT-lattice Boltzmann method. Computers & Mathematics with Applications 79 (1):100–10. doi: 10.1016/J.CAMWA.2017.09.006.
   Web of Science ®Google Scholar
• Brady, J. F., and G. Bossis. 1988. Stokesian dynamics. Annual Review of Fluid Mechanics 20 (1):111–57. doi: 10.1146/annurev.fl.20.010188.000551.
   Web of Science ®Google Scholar
• Ding, E., and C. K. Aidun. 2000. The dynamics and scaling law for particles suspended in shear flow with inertia. Journal of Fluid Mechanics 423:317–44. doi: 10.1017/S0022112000001932.
   Web of Science ®Google Scholar
• Ern, P., F. Risso, D. Fabre, and J. Magnaudet. 2012. Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annual Review of Fluid Mechanics 44 (1):97–121. doi: 10.1146/annurev-fluid-120710-101250.
   Web of Science ®Google Scholar
• Feng, J., H. Hu, and D. Joseph. 1994. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid part 1. Sedimentation. Journal of Fluid Mechanics 261:95–134. doi: 10.1017/S0022112094000285.
   Web of Science ®Google Scholar
• Feng, Z. G., and E. E. Michaelides. 2009. Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows. Computers & Fluids. 38 (2):370–81. doi: 10.1016/j.compfluid.2008.04.013.
   Web of Science ®Google Scholar
• Feng, Z. G., and E. E. Michaelides. 2004. The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems. Journal of Computational Physics. 195 (2):602–28. doi: 10.1016/j.jcp.2003.10.013.
   Web of Science ®Google Scholar
• Gabbanelli, S., G. Drazer, and J. Koplik. 2005. Lattice Boltzmann method for non-Newtonian (power-law) fluids. Physical Review E 72 (4):046312. doi: 10.1103/PhysRevE.72.046312.
   Web of Science ®Google Scholar
• Huang, P. Y., H. H. Hu, and D. D. Joseph. 1998. Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids. Journal of Fluid Mechanics 362:297–325. doi: 10.1017/S0022112098008672.
   Web of Science ®Google Scholar
• Huang, H.,. X. Yang, and X. Lu. 2014. Sedimentation of an ellipsoidal particle in narrow tubes. Physics of Fluids 26 (5):053302. doi: 10.1063/1.4874606.
   Web of Science ®Google Scholar
• Hu, H. H., D. D. Josef, and A. F. Fortes. 1997. Experiments and direct simulations of fluid-particle motion. International Video Journal of Engineering Research 2:17–24.
   Google Scholar
• Hu, H. H., N. Patankar, and M. Y. Zhu. 2001. Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. Journal of Computational Physics. 169 (2):427–62. doi: 10.1006/jcph.2000.6592.
   Web of Science ®Google Scholar
• Jafari, S., R. Yamamoto, and M. Rahnama. 2011. Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions. Physical Review E 83 (2):026702. doi: 10.1103/PhysRevE.83.026702.
   Web of Science ®Google Scholar
• Jahanshahi Javaran, E., M. Rahnama, and S. Jafari. 2013. Investigating the applicability of combined lattice Boltzmann-smoothed profile method in particulate systems. Particulate Science and Technology 31 (6):643–10. doi: 10.1080/02726351.2013.831153.
   Web of Science ®Google Scholar
• Kang, S. K., and Y. A. Hassan. 2011. A comparative study of direct forcing immersed boundary lattice Boltzmann methods for stationary complex boundaries. International Journal for Numerical Methods in Fluids 66 (9):1132–58. doi: 10.1002/fld.2304.
   Web of Science ®Google Scholar
• Karimnejad, S., A. Amiri-Delouei, M. Nazari, M. M. Shahmardan, and A. A. Mohamad. 2018. Sedimentation of elliptical particles using immersed boundary – lattice Boltzmann method: A complementary repulsive force model. Journal of Molecular Liquids. 262:180–93. doi: 10.1016/j.molliq.2018.04.075.
   Web of Science ®Google Scholar
• Koblitzm, A. R., S. Lovett, and N. Nikiforakis. 2018. Direct numerical simulation of particle sedimentation in a Bingham fluid. Physical Review Fluids 3:093302. 10.1103/phesRevFluids.3.093302.
   Web of Science ®Google Scholar
• Kohestani, A., M. Rahnama, S. Jafari, and E. Jahanshahi Javaran. 2020. Non-circular particle treatment in smoothed profile method: A case study of elliptical particles sedimentation using lattice Boltzmann method. Journal of Dispersion Science and Technology 41 (3):315–29. doi: 10.1080/01932691.2019.1572514.
   Web of Science ®Google Scholar
• Ladd, A. J. 1994. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part II. Numerical results. Journal of Fluid Mechanics 271:311–39. doi: 10.1017/S0022112094001783.
   Web of Science ®Google Scholar
• Li, Q., N. Hong, B. Shi, and Z. Chai. 2014. Simulation of power-law fluid flows in two-dimensional square cavity using multi relaxation-time lattice Boltzmann method. Communications in Computational Physics 15 (1):265–84. doi: 10.4208/cicp.160212.210513a.
   Web of Science ®Google Scholar
• Liu, Z., W. B. Cai, L. N. He, N. Nakayama, K. Chen, X. M. Sun, X. Y. Chen, and H. J. Dai. 2007. In vivo bio distribution and highly efficient tumor targeting of carbon nanotubes in mice. Nature Nanotechnology 2 (1):47–52. doi: 10.1038/nnano.2006.170.
   PubMed Web of Science ®Google Scholar
• Luo, X., M. R. Maxey, and G. E. Karniadakis. 2009. Smoothed profile method for particulate flows: Error analysis and simulation. Computers in Physics. 228 (5):1750–69. doi: 10.1016/j.jcp.2008.11.006.
   Web of Science ®Google Scholar
• Mendu, S. S., and P. K. Das. 2012. Flow of power-law fluids in a cavity driven by the motion of two facing lids – A simulation by lattice Boltzmann method. Journal of Non-Newtonian Fluid Mechanics 175–176:10–24. doi: 10.1016/j.jnnfm.2012.03.007.
   Web of Science ®Google Scholar
• Mino, Y., H. Shinto, S. Sakai, and H. Matsuyama. 2017. Effect of internal mass in the lattice Boltzmann simulation of moving solid bodies by the smoothed-profile method. Physical Review E 95 (4-1):043309. doi: 10.1103/PhysRevE.95.043309.
   PubMed Web of Science ®Google Scholar
• Mohamad, A. A. 2011. Lattice Boltzmann method, fundamentals and engineering applications with computer codes. London: Springer.
   Google Scholar
• Nada Kumar, N., and S. Sarathbabu Duvvuri. 2018. Non-Newtonian fluid past irregular particles from low to moderate Reynolds numbers. International Journal of Pure and Applied Mathematics 120 (6):7929–48.
   Google Scholar
• Nakayama, Y., and R. Yamamoto. 2005. Simulation method to resolve hydrodynamic interactions in colloidal dispersions. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 71 (3 Pt 2B):036707. doi: 10.1103/PhysRevE.71.036707.
   PubMed Web of Science ®Google Scholar
• Nguyen, N.-Q., and A. J. C. Ladd. 2002. Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Physical Review E 66 (4):0467081–12. doi: 10.1103/PhysRevE.66.046708.
   Web of Science ®Google Scholar
• Nie, D. M., and J. Lin. 2010. A LB-DF/FD method for particle suspensions. Communications in Computational Physics 7 (3):544–63. doi: 10.4208/cicp.2009.08.155.
   Web of Science ®Google Scholar
• Nie, D. M., and J. Lin. 2011. Dynamics of two elliptical particles sedimentation in a vertical channel: Chaotic state. International Journal of Fluid Dynamics. 25 (7):401–6. doi: 10.1080/10618562.2011.613829.
   Web of Science ®Google Scholar
• Nitin, S., and R. P. Chhabra. 2006. Sedimentation of a circular disk in power law fluids. Journal of Colloid and Interface Science 295 (2):520–7. doi: 10.1016/j.jcis.2005.08.024.
   PubMed Web of Science ®Google Scholar
• Peskin, C. S. 1972. Flow patterns around heart valves, a numerical method. Journal of Computational Physics 10:251–71. 10.1016/0021-9991(72)90065-4.
   Web of Science ®Google Scholar
• Rajitha, P., R. P. Chhabra, N. E. Sabiri, and J. Comiti. 2006. Drag on non-spherical particles in power law non-Newtonian media. International Journal of Mineral Processing 78 (2):110–21. doi: 10.1016/j.minpro.2005.09.003.
   Google Scholar
• Shao, B., G. R. Liu, T. Lin, X. George, and X. Yan. 2017. Rotation and orientation of irregular particles in viscous fluids using the gradient smoothed method (GSM). Engineering Applications of Computational Fluid Mechanics 11 (1):557–75. doi: 10.1080/19942060.2017.1329169.
   Web of Science ®Google Scholar
• Sivakumar, P., R. Prakash Bharti, and R. P. Chhabra. 2007. Steady flow of power-law fluids across an unconfined elliptical cylinder. Chemical Engineering Science 62 (6):1682–702. doi: 10.1016/j.ces.2006.11.055.
   Web of Science ®Google Scholar
• Sobhani, S. M. J., S. Bazargan, and K. Sadeghy. 2019. Sedimentation of an elliptic rigid particle in a yield-stress fluid: A lattice-Boltzmann simulation. Physics of Fluids 31 (8):081902. doi: 10.1063/1.5111633.
   Web of Science ®Google Scholar
• Stewart, J. 2007. Calculus. 6th ed. Boston: Brooks Cole.
   Google Scholar
• Succi, S. 2001. The lattice Boltzmann equation for fluid dynamics and beyond. New York: Oxford University Press.
   Google Scholar
• Sullivan, S. P., L. F. Gladden, and M. L. Johns. 2006. Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques. Journal of Non-Newtonian Fluid Mechanics. 133 (2–3):91–8. doi: 10.1016/j.jnnfm.2005.11.003.
   Web of Science ®Google Scholar
• Walayat, K., Z. Zhang, K. Usman, J. Chang, and M. Liu. 2018. Dynamics of elliptical particle sedimentation with thermal convection. Physics of Fluids 30 (10):103301. doi: 10.1063/1.5051817.
   Web of Science ®Google Scholar
• Xia, Z., K. W. Connington, S. Rapak, P. Yue, J. J. Feng, and S. Chen. 2009. Flow patterns in the sedimentation of an elliptical particle. Journal of Fluid Mechanics 625:249–72. doi: 10.1017/S0022112008005521.
   Web of Science ®Google Scholar